On the complexity of open shop scheduling with time lags

TL;DR

This paper proves that minimizing total completion time in a two-machine open shop scheduling problem with unit-time operations is strongly NP-hard, resolving a long-standing open question in computational complexity.

Contribution

It establishes the NP-hardness of total completion time minimization for two-machine open shop with unit-time operations, an open problem in scheduling theory.

Findings

Minimizing total completion time is strongly NP-hard for two-machine open shop with unit-time operations.

The result answers a long-standing open question in the complexity of scheduling problems.

Abstract

The minimization of makespan in open shop with time lags has been shown NP-hard in the strong sense even for the case of two machines and unit-time operations. The minimization of total completion time however has remained open for that case though it has been shown NP-hard in the strong sense for weighted total completion time or for jobs with release dates. This note shows that the minimization of total completion time for two machines and unit-time operations is NP-hard in the strong sense which answers the long standing open question.